I know this sounds like a really stupid question, but are you sure your finger isn't over the camera? Don't get mad, just checking...
You mentioned that the stock camera also saves blank photos, before you take the picture does the image show up on the screen?
The DX has a physical shutter, it is possible the timing of the shutter is physically messed up and the apps capture the image while the shutter is closed, not sure if any apps have this, but you can try messing with the timing of the shutter exposure... I have an issue with the default camera app that it captires the image .5 sec after the flash on the first picture, so sometimes the software and hardware can get out of sync...
I'd say if you find that the shutter's physical timing is off, it might be best to return it as a defective unit...